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« Tulisan terakhir oleh Roni pada November 21, 2023, 04:45:28 PM »
\[ _{11}^{15}\text{Na}^{3-} \]
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« Tulisan terakhir oleh Roni pada September 29, 2023, 06:42:44 PM »
Jarak Euclidean Titik, Garis, dan Bidang di $\mathbb{R}^3$ Sistem Koordinat Cartesian
Jarak antara titik $(a_x,a_y,a_z)$ dan titik $(b_x,b_y,b_z)$ adalah
\[ d_{00}=\sqrt{(a_x-b_x)^2+(a_y-b_y)^2+(a_z-b_z)^2}. \]
Jarak antara titik $(a_x,a_y,a_z)$ dan garis $\frac{x-x_0}{v_x}=\frac{y-y_0}{v_y}=\frac{z-z_0}{v_z}$ adalah
\[ d_{01}=\sqrt{\frac{[(a_y-y_0)v_z-(a_z-z_0)v_y]^2+[(a_z-z_0)v_x-(a_x-x_0)v_z]^2+[(a_x-x_0)v_y-(a_y-y_0)v_x]^2}{{v_x}^2+{v_y}^2+{v_z}^2}}. \]
Jarak antara titik $(a_x,a_y,a_z)$ dan bidang $N_xx+N_yy+N_zz+C=0$ adalah
\[ d_{02}=\frac{|a_xN_x+a_yN_y+a_zN_z+C|}{\sqrt{{N_x}^2+{N_y}^2+{N_z}^2}}. \]
Jarak antara garis $\frac{x-x_0}{v_x}=\frac{y-y_0}{v_y}=\frac{z-z_0}{v_z}$ dan garis $\frac{x-x_1}{w_x}=\frac{y-y_1}{w_y}=\frac{z-z_1}{w_z}$ adalah
\[ d_{11}=\frac{|(x_0-x_1)(v_yw_z-v_zw_y)+(y_0-y_1)(v_zw_x-v_xw_z)+(z_0-z_1)(v_xw_y-v_yw_x)|}{\sqrt{(v_yw_z-v_zw_y)^2+(v_zw_x-v_xw_z)^2+(v_xw_y-v_yw_x)^2}} \]
apabila $v_yw_z\neq{v_zw_y}$ atau $v_zw_x\neq{v_xw_z}$ atau $v_xw_y\neq{v_yw_x}$.
Apabila $v_yw_z=v_zw_y$ dan $v_zw_x=v_xw_z$ dan $v_xw_y=v_yw_x$, maka
\[ d_{11}=\sqrt{\frac{[(y_0-y_1)v_z-(z_0-z_1)v_y]^2+[(z_0-z_1)v_x-(x_0-x_1)v_z]^2+[(x_0-x_1)v_y-(y_0-y_1)v_x]^2}{{v_x}^2+{v_y}^2+{v_z}^2}}. \]
Jarak antara garis $\frac{x-x_0}{v_x}=\frac{y-y_0}{v_y}=\frac{z-z_0}{v_z}$ dan bidang $N_xx+N_yy+N_zz+C=0$ adalah
\[ d_{12}=\frac{|x_0N_x+y_0N_y+z_0N_z+C|}{\sqrt{{N_x}^2+{N_y}^2+{N_z}^2}} \]
apabila $N_xv_x+N_yv_y+N_zv_z=0$.
Apabila $N_xv_x+N_yv_y+N_zv_z\neq0$, maka $d_{12}=0$.
Jarak antara bidang $N_xx+N_yy+N_zz+C=0$ dan bidang $kN_xx+kN_yy+kN_zz+C^\prime=0$ adalah
\[ d_{22}=\frac{C-(C^\prime/k)}{\sqrt{{N_x}^2+{N_y}^2+{N_z}^2}}. \]
Jarak antara bidang $N_xx+N_yy+N_zz+C=0$ dan bidang $M_xx+M_yy+M_zz+C^\prime=0$ adalah
\[ d_{22}=0 \]
apabila $N_yM_z\neq{N_zM_y}$ atau $N_zM_x\neq{N_xM_z}$ atau $N_xM_y\neq{N_yM_x}$.
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« Tulisan terakhir oleh katarinakohler pada April 15, 2023, 12:32:23 AM »
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« Tulisan terakhir oleh katarinakohler pada April 15, 2023, 12:30:56 AM »
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« Tulisan terakhir oleh MeadeDorian pada April 10, 2023, 10:27:22 AM »
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« Tulisan terakhir oleh MeadeDorian pada April 10, 2023, 10:25:24 AM »
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« Tulisan terakhir oleh MeadeDorian pada April 10, 2023, 10:23:00 AM »
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